Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
536 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 131 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22618835 | C2 | semidirect |
| 2. #22612143 | C2 | semidirect |
| 3. #22612104 | C2 | semidirect |
| 4. #22612004 | C2 | semidirect |
| 5. #22611876 | C2 | semidirect |
| 6. #22611827 | C2 | semidirect |
| 7. #22611747 | C2 | semidirect |
| 8. C73×#3176 | C2 | semidirect |
| 18. #17988409 | C22 | semidirect |
| 19. #17988408 | C22 | semidirect |
| 20. #17988400 | C22 | semidirect |
| 23. #17988365 | C22 | semidirect |
| 25. #499×C73 | C22 | semidirect |
| 26. #493×C73 | C22 | semidirect |
| 30. #442×C73 | C22 | semidirect |
| 167. #3176 | D73 | semidirect |
| 175. C73 | #33692 | semidirect |
| 180. #499 | C2×D73 | semidirect |
| 181. #493 | C2×D73 | semidirect |
| 189. #442 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618835 | 2 |
| #22612143 | 2 |
| #22612104 | 2 |
| #22612004 | 2 |
| #22611876 | 2 |
| #22611827 | 2 |
| #22611747 | 2 |
| C73×#3176 | 2 |
| #33692 | 73 |